imperfect tense

In Barron's 501 Arabic Verbs, the author refers to the following examples as conjugated in the "imperfect":
هو يكتب
نحن نقيم
هم يقولون

According to Wikipedia, the imperfect combines past tense (reference to a past time) and imperfective aspect (e.g., "was walking" or "used to walk"). However, as I understand, the above conjugations do not have a past tense aspect. They translate in the present tense, as:
He writes
We stay
They say

Wouldn't the book therefore be clearer if it referred to the above conjugations as "present" rather than "imperfect," since they do not mean:
He used to write
We used to stay
They used to say

In Barron's 501 Arabic Verbs, the author refers to the following examples as conjugated in the "imperfect":
هو يكتب
نحن نقيم
هم يقولون

According to Wikipedia, the imperfect combines past tense (reference to a past time) and imperfective aspect (e.g., "was walking" or "used to walk"). However, as I understand, the above conjugations do not have a past tense aspect. They translate in the present tense, as:
He writes
We stay
They say

Wouldn't the book therefore be clearer if it referred to the above conjugations as "present" rather than "imperfect," since they do not mean:
He used to write
We used to stay
They used to say

^ Hopefully, in due course you will find out that Arabic mindset does not map exactly onto the way we think of English grammar, for example. What you have quoted is correct and what you say is correct too! it is, as ayed has indicated, context dependent. There are various devices employed which set the scene, so to speak and with these one has a fairly good idea where we are within the confines of time.

The problem here is that the words “perfect” and “imperfect” are used in entirely different meanings in Indo-European and in Semitic studies. In Indo-European languages they refer to the imperfective and imperfective aspects of verbs referring to the past. In Semitic studies “perfect” means complete (past), and “imperfect” means incomplete (present or future). I know it is confusing. Can I give you some advice? You will never learn Arabic browsing around dodgy internet sites. Buy a proper textbook and work through it from start to finish.

According to the author of 501 Arabic Verbs, the perfect refers to a completed action and the imperfect refers to an uncompleted action. Neither the perfect nor the imperfect refer to tense in Arabic. In fact, there can be past, present and future in both the perfect and imperfect. For example:

I was summarizing. But he does say that both the perfect and imperfect may refer to past, present and future actions. Here is what he says on p. ix-x:
“Thus كَتَبَ, in the perfect, can, depending on the context, mean “he wrote” or “he had written” (completed acts in the past), or “he will have written” (completed act in the future); but it cannot be used to mean “was writing” (uncompleted act in the past). Likewise, the imperfect يَكْتُبُ can indicate future, when it occurs with no other marker, but it is quite commonly used for the present, which does not have a tense of its own in Arabic; it only unambiguously indicates future when it has the prefix سَ or is preceded by the word سَوفَ, or when the sentence includes some other indicator of tense. Thus, depending on the context, يَكْتُبُ could mean “was writing” (uncompleted act in the past), “will be writing” (uncompleted act in the future), or “is writing” (an act in the present, therefore by definition uncompleted).”

I was summarizing. But he does say that both the perfect and imperfect may refer to past, present and future actions. Here is what he says on p. ix-x:
“Thus كَتَبَ, in the perfect, can, depending on the context, mean “he wrote” or “he had written” (completed acts in the past), or “he will have written” (completed act in the future); but it cannot be used to mean “was writing” (uncompleted act in the past). Likewise, the imperfect يَكْتُبُ can indicate future, when it occurs with no other marker, but it is quite commonly used for the present, which does not have a tense of its own in Arabic; it only unambiguously indicates future when it has the prefix سَ or is preceded by the word سَوفَ, or when the sentence includes some other indicator of tense. Thus, depending on the context, يَكْتُبُ could mean “was writing” (uncompleted act in the past), “will be writing” (uncompleted act in the future), or “is writing” (an act in the present, therefore by definition uncompleted).”

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It seems right to me. Generally speaking فَعَلَ (past, perfect, الماضي, whatever you want to call them) verbs refer to actions that are completed (with respect to the present or some particular time frame), while يَفْعَلُ (present, imperfect, الحاضر) verbs refer to actions that are uncompleted (with respect to some particular time frame).

I will have to review my grammar terminology, as I'm not sure I completely understand exactly what perfect, imperfect, aspect, et. al. mean in terms of grammar. Suffice it to say that the exact meaning of each term will vary depending on language. As others have noted, their use in English grammar will not completely overlap that of Arabic.

This is also wrong. yaktubu on its own cannot mean "he was writing". It can only have this meaning in the phrase kaana yaktubu, or in a Haal clause.

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Right, it can't mean that on it's own, but in certain contexts, such as the ones you noted. That may be what the author meant by "depending on context." Perhaps he was not as clear as he could have been.

I think your book is full of nonsense.

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No need to throw the baby out with the bath water. I actually have the same book and, his explanation of verb forms and meanings aside, it is a good resource for showing the verb conjugations, which include sample sentences to show verbs in context.